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Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions -- such as random rectangles or histograms -- each describing a portion of the…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…
We address the challenges of modeling high-frequency integer price changes in financial markets using continuous distributions, particularly the Student's t-distribution. We demonstrate that traditional GARCH models, which rely on…
We study the critical points of the likelihood function over the Fermat hypersurface. This problem is related to one of the main problems in statistical optimization: maximum likelihood estimation. The number of critical points over a…
Observational studies of halo stars during the last two decades have placed some limits on the quantity and nature of accreted dwarf galaxy contributions to the Milky Way stellar halo by typically utilizing stellar phase-space information…
A flood of reliable seismic data will soon arrive. The migration to larger telescopes on the ground may free up 4-m class instruments for multi-site campaigns, and several forthcoming satellite missions promise to yield nearly uninterrupted…
Traditional solar flare forecasting approaches have mostly relied on physics-based or data-driven models using solar magnetograms, treating flare predictions as a point-in-time classification problem. This approach has limitations,…
We propose a likelihood ratio based inferential framework for high dimensional semiparametric generalized linear models. This framework addresses a variety of challenging problems in high dimensional data analysis, including incomplete…
We present a new determination of the star-forming main sequence (MS), obtained through stacking 100k K-band-selected galaxies in the far-infrared (FIR) Herschel and James Clerk Maxwell Telescope (JCMT) imaging. By fitting the dust emission…
We introduce the problem of hidden Hamiltonian cycle recovery, where there is an unknown Hamiltonian cycle in an $n$-vertex complete graph that needs to be inferred from noisy edge measurements. The measurements are independent and…
We have used over 10,000 early-type galaxies from the 6dF Galaxy Survey (6dFGS) to construct the Fundamental Plane across the optical and near-infrared passbands. We demonstrate that a maximum likelihood fit to a multivariate Gaussian model…
Variable selection in cluster analysis is important yet challenging. It can be achieved by regularization methods, which realize a trade-off between the clustering accuracy and the number of selected variables by using a lasso-type penalty.…
In order to attain a statistical description of the evolution of cosmic density fluctuations in agreement with results from the numerical simulations, we introduce a probability conditional formalism (CF) based on an inventory of isolated…
Using combinations of H\alpha, ultraviolet (UV), and infrared (IR) emission, we estimate the star formation rate (SFR) surface density, \Sigma_SFR, at 1 kpc resolution for 30 disk galaxies that are targets of the IRAM HERACLES CO survey. We…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
We propose a variant of the Rapidly Exploring Random Tree Star (RRT$^{\star}$) algorithm to synthesize trajectories satisfying a given spatio-temporal specification expressed in a fragment of Signal Temporal Logic (STL) for linear systems.…
JWST have revealed temporarily-quenched and ultraviolet-luminous galaxies in the early universe, suggesting enhanced star formation stochasticity. Verifying this hypothesis is critical, yet challenging; outshining, wherein light from young…
We are totally immersed in the Big Data era and reliable algorithms and methods for data classification are instrumental for astronomical research. Random Forest and Support Vector Machines algorithms have become popular over the last few…
The detection and estimation of gravitational wave burst signals, with {\em a priori} unknown polarization waveforms, requires the use of data from a network of detectors. For determining how the data from such a network should be combined,…